Fixing with @TallTed fixes

index.bs

@@ -134,9 +134,9 @@ asserts a logical negation. The examples below will use a sheet of paper with a
 as a negative surface.
 
 An empty *negative surface* on the default positive surface expresses a logical contradicton. When there are one
-or more RDF graphs written on an *negative* surface they mean the negation of those RDF graphs.
+or more RDF graphs written on a *negative* surface, they mean the negation of those RDF graphs.
 
-A blank node on a negative surface is interpreted as a universal quantified variable. The reason is 
+A blank node on a negative surface is interpreted as an universal quantified variable. The reason is 
 that:
 
 ```
@@ -316,7 +316,7 @@ A surface can be queried by providing a query surface with the `log:onNegativeAn
 
 `:Ghent a :City` is a triple on the implicit positive surface. The two nested
 negative surfaces express that for any subject `_:S` on the positive service
-that is a `:City`, it implies that `_:S` needs be be also a `:HumanCommunity`.
+that is a `:City`, it is implied that `_:S` if also a `:HumanCommunity`.
 
 <pre highlight="turtle">
 @prefix ex: &lt;http://example.org/ns#&gt;.
@@ -388,7 +388,7 @@ Surface {#Surface}
 Surfaces are written as triples where the `subject` is a list of zero or more blank nodes. 
 The `object` is a RDF graph or the `true` or `false` literal. The blank nodes in the 
 subject list are treated as marks on the object RDF graph. The `predicate` specifies 
-the kind of surface. Any kind of surface may be used but the following built-in have 
+the kind of surface. Any kind of surface may be used, but the following built-ins have 
 special semantics:
 
 <table>
@@ -406,7 +406,7 @@ special semantics:
 </table>
 
 A surface can contain zero or more other surfaces. These surfaces are then nested.
-Nested surfaces can share the same [[URI]]-s and literals (by copying the data), 
+Nested surfaces can share the same [[URI]]s and literals (by copying the data), 
 but can't share blank nodes. Any blank nodes that are written inside a surface 
 (not as subject of an RDF Surface) are to be interpreted as *coreferences* to the
 blank node graffiti defined on a parent RDF Surface. If no such parent RDF Surface
@@ -554,7 +554,7 @@ As RDF Surface:
 
 </div>
 
-In RDF Surfaces an default positive surface is implicitly assumed for each RDF document. On this default positive surface all existential variables are implicitly quantified. Example 20 can be rewritten as:
+In RDF Surfaces, a default positive surface is implicitly assumed for each RDF document. On this default positive surface, all existential variables are implicitly quantified. Example 20 can be rewritten as:
 
 <div class="example">
 A default positive surface with an implicit `_:X` existential variable.
@@ -569,7 +569,7 @@ _:X :knows :Alice .
 
 </div>
 
-When a blank node is marked on an odd nested negative surface, then it is interpreted as an universal quantified variable in the scope of the nested surface.
+When a blank node is marked on an odd nested negative surface, it is interpreted as an universal quantified variable in the scope of the nested surface.
 
 <div class="example">
 The surface below should be interpreted as : "Every person knows Alice".
@@ -607,7 +607,7 @@ As RDF Surface:
 ## Negative Surface ## {#NegativeSurface}
 
 A negative surface is an RDF graph which claims that an RDF Graph on it is false. The
-intepretation of the negative surface is the negation of RDF Graph on it. 
+interpretation of the negative surface is the negation of RDF Graph on it. 
 
 The semantics of a negative surface is interpreted as a logical falsehood:
 
@@ -746,7 +746,7 @@ As RDF Surface:
 
 </div>
 
-With combinations of AND and NOT other logical truth function can be build. E.g.
+With combinations of AND and NOT other logical truth function can be built. E.g.
 
 - Disjunction: `P ∨ Q` : `NOT( NOT(P) AND NOT(Q))`
 - Material implication `P → Q` : `NOT( P AND NOT Q )` .